Explanation

The differential equation xy' = y can be rewritten as y'/y = 1/x.

This equation has a unique solution when x ≠ 0, since dividing by zero is undefined.

The solution exists on the region defined by either x > 0 or x < 0.

Explanation

When Thorium (Th) emits a beta particle (β⁻), a neutron converts into a proton, increasing atomic number by 1.

So Thorium (Z=90) becomes Protactinium (Z=91).

Explanation

A bimodal distribution has two modes, meaning two values occur with the highest and equal frequency.

It indicates the presence of two peaks in the data set.

Explanation

Imam Ali (R.A) compared the mind of a newborn child to vacant land, emphasizing the role of upbringing and environment.

This view supports the idea that a child’s mind is shaped by experiences and education.

Explanation

Valuing is the stage where an individual shows appreciation or commitment to a value, idea, or behavior.

It reflects recognition of worth and personal acceptance of an objective or idea.

Explanation

Two parallel conductors carrying current in the same direction attract each other due to magnetic fields they produce.

If currents flow in opposite directions, the force would be repulsive.

Explanation

Given ∫12x⁻⁵ √(-3x⁻⁴ + 1) dx

Let u = -3x⁻⁴ + 1

du/dx = 12x⁻⁵

du = 12x⁻⁵ dx

∫√u du = ∫u^(1/2) du

= (2/3)u^(3/2) + C

Substituting back u = -3x⁻⁴ + 1:

= (2/3)(-3x⁻⁴ + 1)^(3/2) + C

Explanation

Explanation

The absorption of X-rays in a given material follows an exponential curve, described by the Beer-Lambert law:

I(x) = I₀ × e^(-μx)

where I(x) is the intensity of the X-rays after passing through a thickness x of the material, I₀ is the initial intensity, μ is the linear attenuation coefficient, and x is the thickness of the material.

Explanation

Orbital electrons have specific, quantized energy levels depending on their orbit.

They cannot have arbitrary energy values — only fixed amounts allowed by quantum rules.